GB2487571A

GB2487571A - Rearrangement of geographical network map into a more compact topological form by moving network nodes towards the map's centre using overlaidcells

Info

Publication number: GB2487571A
Application number: GB1101449.5A
Authority: GB
Inventors: Gerard Terence Foster; John William Hern
Original assignee: Aircom International Ltd
Current assignee: Aircom International Ltd
Priority date: 2011-01-28
Filing date: 2011-01-28
Publication date: 2012-08-01
Also published as: WO2012101445A1; GB201101449D0

Abstract

Geographical maps of networks often include high density areas of information corresponding to towns separated by substantially empty low density rural areas. Hence the detail of the urban areas is lost when zoomed out to view the whole network (Fig. 2) or the overall network is invisible when zoomed in to view the urban detail (Fig. 3). The invention superimposes and array of cells (eg. square grid or hexagons) over the map (Fig. 5) and associates sites/nodes with cells. A predetermined cell, typically the most central, is identified and the cells are polled to determine whether they are occupied by network sites. This typically starts with the predetermined cell and moves outwards in concentric rings (Figs. 4-11). Where a cell is occupied it is further determined whether cells between it and the predetermined cell are occupied. The sites are moved into cells closer to the predetermined cell if they are unoccupied. This collapses the blank unoccupied areas and produces a more compact network representation that still retains some relative geographical information.

Description

NETWORKS

The present disclosure relates to representation of networks.

A number of academic papers, telecoms journals and standardisation bodies address the topic of modelling networks, such as teleconirnunications networks, using so-called nodes and edges. In this context, nodes can be thought of as modelled representations of distinct physical..pieces of electronic.. equipment and edges can be.thought of as physical and/or virtual interconnections between the nodes.

in the context of designing telecommunications networks (telecoms networks), node and edge-based modelling of telecoms networks is typically employed to plan upgrades and/or expansions to the network ahead of making a decision to implement an upgrade or expansion and starting to incur capital expenditure. Thus, modelling of such networks can be a cost effective way to plan.

As telecoms networks have grown in size and computer visualisations have evolved, many telecoms networks are now modelled as extremely comprehensive interactive models with detailed visualisations, often across multiple layers of technology and with tens of thousands of nodes at a time.

One technique for visualising a network is to use a geography-based layout. In this technique, nodes of a network may be displayed in a similar manner to a geographical map.

However, a geography-based layout is general].y not well suited for many types of network, particularly where the nodes are unevenly distributed and where there are many nodes at the same location. For example, graphs of telecom networks, especially those relating to mobile telecommunications, tend to suffer greatly from uneven distribution of nodes; network equipment tends to be located predominantly within the boundaries of towns and cities, with little network equipment being located in more rural areas.

Using a simple geographic layout to represent such networks tends to result in a lot of white space between the nodes, making it harder for the user to understand the relationships between nodes and gain a useful insight from the visualisations. In such a situation, typically a user will either have to zoom out so far that is difficult to see individual nodes, or the user may only be able to view a small part of the overall graph on a display at any one time.

An approach which may be used to try to reduce the size of a network is to try to ensure that graphs are drawn with edges of a near-equal length, typically by using so-called force-based (force-directed) algorithms. An example of a force based algorithm is described in Kamada T. "Visualising Abstract Objects and Relations", World Scientific, 1989, pages 73 to 82. Force-based algorithms tend to produce aesthetically-pleasing results and are flexible enough that they can be applied to a wide range of network types. 1-lowever, they are typically not well suited for use with a telecoms network as they do not scale well; the computation time and resources needed to simulate the forces for a large number of nodes (e.g.> 10,000 S nodes) tends to be large due to the complexity of calculating the interacting forces. Force-based algorithms tend to work best when simulating the forces between fewer than one hundred nodes. This is. at.. least three orders. of magnitude..too..small.for use with telecoms networks, which typically have tens of thousands of nodes.

In a first aspect, there is provided a computer implemented method for generating a representation of a network having a plurality of sites, the method comprising: generating an array comprising a plurality of cells; arranging the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; querying each cell of the array in a predetermined order so as to detect whether each cell is occupied by one or more sites of the network; and for each cell that is detected as being occupied, moving the sites associated with the occupied cell to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied.

In a second aspect, there is provided apparatus for generating a representation of a network having a plurality of sites, the apparatus comprising: means for generating an array comprising a plurality of cells; means for arranging the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; means for querying each cell of the array in a predetermined order so as to detect whether each cell is occupied by one or more sites of the network; and means for moving, for each cell that is detected as being occupied, the sites associated with the occupied cell to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied.

In a third aspect, there is provided a device for generating a representation of a network having a plurality of sites, the device comprising: array generating logic operable to generate an array comprising a plurality of cells; cell arrangement logic operable to arrange the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; a detector operable to query each cell of the array in a predetermined order so as to detect whether each cell is occupied by one or more sites of the network; and site moving logic operable to move, for each cell that is detected as being occupied, the sites associated with the occupied cell to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied.

S In a fourth aspect, there is provided apparatus for generating a representation of a network having a plurality of sites, the apparatus comprising logic programmed to carry out the. steps of:.. generating an. array comprising a plurality of cells;., arranging. the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defmed with respect to the network; querying each cell of the array in a predetermined order so as to detect whether each cell is occupied by one or more sites of the network; and moving, for each cell that is detected as being occupied, the sites associated with the occupied cell to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied.

Accordingly, a representation of a network having a plurality of sites may be efficiently generated so as to have a reduced size.

In a fifth aspect, there is provided a method for reducing a displayed size of a representation of a network having a plurality of sites, the method comprising: overlaying a grid having a plurality of cells over the sites of the network so that at least some of the cells correspond to sites of the network, the cells which correspond with sites being associated with those sites; detecting, in a predetermined order, which cells are occupied by sites; and moving sites associated with occupied cells towards unoccupied cells closer to a predetermined cell so as to generate a representation of the network which has a reduced size and which substantially maintains an overall visual impression of relative locations of the sites of the network.

In a sixth aspect, there is provided apparatus for reducing a displayed size of a representation of a network having a plurality of sites, the apparatus comprising: means for overlaying a grid having a plurality of cells over the sites of the network so that at least some of the cells correspond to sites of the network, the cells which correspond with sites being associated with those sites; means for detecting, in a predetermined order, which cells are occupied by sites; and means for moving sites associated with occupied cells towards unoccupied cells closer to a predetermined cell so as to generate a representation of the network which has a reduced size and which substantially maintains an overall visual impression of relative locations of the sites of the network.

Accordingly, a representation of the network may be generated efficiently which has a reduced size and which substantially maintains an overall visual impression of relative locations of the sites of the network.

In a seventh aspect, there is provided a computer implemented method for generating a representation of a network having a plurality of sites, the method comprising: generating an array comprising a plurality of cells, the array comprising a plurality of concentric subsets of cells arranged concentrically around the. predetermined cell,., each concentric subset having, a respective radius associated with a distance of the cells of that subset from the predetermined cell; arranging the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; querying each cell of the array so as to detect whether each cel1 is occupied by one or more sites of the network, the querying comprising: first querying cells of a concentric subset having the smallest radius; and then querying cells of subsequent concentric subsets in order of is increasing radius; and for each cell that is detected as being occupied, moving the sites associated with the occupied cell to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied.

In an eighth aspect, there is provided apparatus for generating a representation of a network having a plurality of sites, the apparatus comprising: means for generating an array comprising a plurality of cells, the array comprising a plurality of concentric subsets of cells arranged concentrically around the predetermined cell, each concentric subset having a respective radius associated with a distance of the cells of that subset from the predetermined cell; means for arranging the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; means for querying each cell of the array so as to detect whether each cell is occupied by one or more sites of the network, the querying comprising: first querying cells of a concentric subset having the smallest radius; and then querying cells of subsequent concentric subsets in order of increasing radius; and for each cell that is detected as being occupied, means for moving the sites associated with the occupied cell to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied.

Accordingly, a representation of a network having a plurality of sites may be generated efficiently so as to have a reduced size.

In a ninth aspect, there is provided a computer implemented method for generating a representation of a network having a plurality of sites, the method comprising: generating an array comprising a plurality of cells; arranging the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; querying a first cell of the array so as to detect whether that cell is occupied by one or more of the network; querying a next cell of the array according to a predetermined order if the first cell is detected as not being occupied; detecting whether there arc any unoccupied cells closer to the predetermined cell than the first cell if the first cell is detected as being occupied; and moving the sites associated with the first cell to an unoccupied cell closer to the predetermined cell than the first cell if it is detected that there are one or more unoccupied cells closer to the predetermined cell than the first cell.

In a tenth aspect, there is provided apparatus for generating a representation of a network having a plurality of sites, the apparatus comprising: means for generating an array comprising a plurality of cells; means for arranging the cells of the array with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network; means for querying a first cell of the array so as to detect whether that cell is occupied by one or more sites of the network; means for querying a next cell of the array according to a predetermined order if the first cell is detected as not being occupied; means for detecting whether there are any unoccupied cells closer to the predetermined cell than the first cell if the first cell is detected as being occupied; and means for moving the sites associated with the first cell to an unoccupied cell closer to the predetermined cell than the first cell if it is detected that there are one or more unoccupied cells closer to the predetermined cell than the first cell. Accordingly, a representation of a network having a plurality of sites may be efficiently generated so as to have a reduced size.

Various other respective aspects and features of the invention are defined in the appended claims.

Detailed examples will now be described by way of example with reference to the accompanying drawings, in which: Figure 1 is a schematic diagram of a geography based layout of a telecoms network; Figure 2 is a schematic diagram of a geography based layout of a telecoms network displayed on a computer display; Figure 3 is a schematic diagram of a geography based layout of a telecoms network partially displayed on a computer display; Figure 4 is a schematic diagram of a representation of a network; Figure 5 is a schematic diagram of an array of cells in combination with a representation of a network; Figures 6 to 11 illustrate the movement of sites of the network; Figure 12 is diagram of a compressed representation of the network illustrated in Figure 4; Figure 13 schematically illustrates a reduction in size of the representation of the network; Figure 14 is a flow chart of a method for generating a representation of a network; Figure 15 is a flow chart of a method for generating a representation of a network; Figure 16 is a schematic diagram of a hexagonal array of cells used to generate a representation of a network; and Figure 17 is a schematic diagram of a computer system.

A method, apparatus, device, software and storage medium for generating a representation of a network are disclosed. In the following description, a number of specific details are presented in order to provide a thorough understanding. It will be apparent however to a person skilled in the art that these specific details need not be employed to practise the present disclosure. Conversely, specific details known to the person skilled in the art are omitted for the purposes of clarity in presenting the disclosure.

Figure 1 schematically illustrates a geography based layout of a telecoms network 10.

In particular, the network 10 comprises nodes, such as nodes 12, 14, 16, 18 and 20. As mentioned above, nodes of a telecoms network can be thought of as being physical devices located at a physical position in the environment. In the example of Figure 1, the positions of the nodes represent the physical locations of physical devices. A node may be connected to one or more other nodes by edges. As mentioned above, in the context of a telecoms network, edges can be thought of as physical andlor virtual interconnections between the nodes. For example, node 18 is connected to node 20 by an edge 22. However, it will be appreciated that nodes may be connected by one or more edges in any appropriate maimer. In the context of a tclccoms network, "connected" should be understood to mean that data can be communicated between the nodes.

When designing a tclecoms network, a user may wish to view the nodes and edges of the network so that they can plan alterations to the network, such as network upgrades, addition/subtraction of nodes andlor edges and the like. As mentioned above, a user may cause a representation of the network 10 to be displayed on a display of a computer. This is illustrated in Figure 2.

Figure 2 schematically shows the network 10 being displayed on a display 28 of a computer 30 using known techniques. However, as shown in Figure 2, if there are a large number of nodes, it may be difficult to display all the nodes and edges of the network 10 in sufficient detail and at a resolution that enables the user to understand details of the network 10. Accordingly, a user may wish to zoom in to view only part of the network. This is illustrated in Figure 3.

Figure 3 schematically illustrates display of a portion of the network 10 on the display 28. However, as can be seen from Figure 3, it may be difficult for the user to understand the relationships between the nodes and edges because only part of the network can be viewed in the "zoomed in" view. Therefore, a user may have to pan and scroll around the network and/or zoom in and out in order to view details of the network which are of interest.

Is The situation illustrated with respect to Figures 1 to 3 may arise when the nodes are represented in such a way as to m.ap to physical locations in the physical environment. As mentioned above, such a representation may lead to a significant amount of space between the nodes. Additionally, as mentioned above, techniques such as force based algorithms may be unsuitable when there are a large number of nodes due to the significant processing resources needed to implement such algorithms and limitations within the algorithms themselves.

Therefore, the present disclosure provides teachings of an alternative approach in which a grid having a plurality of cells is overlaid over the sites of the network so that at least some of the cells correspond to sites of the network, the cells which correspond with sites being associated with those sites, and detecting, in a predetermined order, which cells are occupied by sites. In some examples, each of the sites comprises one or more telecoms nodes and the number of cells in the grid is arranged so that the number of occupied cells is less than the number of unoccupied cells by greater than a predetermined threshold. Examples of the present disclosure move sites associated with occupied cells towards unoccupied cells closer to a predetennined cell so as to generate a representation of the network which has a reduced size and which substantially maintains an overall visual impression of relative locations of the sites of the network.

Examples will now be described in more detail with reference to Figures 4 to 13. In the following, the examples are implemented by a general purpose computer system comprising a processor, a memory, a display, one or more input devices, a hard disk drive and the like, although it will be appreciated that the computer system could comprise any suitable elements for enabling the examples to be implemented. The general purpose computer will be described in more detail later below with reference to Figure 17. However, it will be appreciated that any suitable computer, network workstation, and the like could be used to implement the examples described herein. Additionally, it will be appreciated that the examples may be implemented on one or more devices or apparatus having suitable logical elements (e;g. one or more field progranimablegate arrays FPGA and the like) or apparatusor one or more devices comprising logic operable to carry out the methods of the examples described herein.

Figure 4 is a schematic diagram of a representation of a network 20. In particular, the network comprises a plurality of sites, such as site 50, site 52, site 54, site 56, site 74 and site 76. In these examples, a site represents one or more items of network equipment located at that site. In other words, a site can be thought of as comprising one or more nodes as described above. In the representation shown in Figure 4, site 50 is connected to site 52 by an is edge 58 and to site 56 by an edge 60. Site 50 is also connected to other sites of the network 20 as shown in Figure 4. Site 52 is connected to site 54 by an edge 62, and site 54 is connected to site 56 by an edge 64. It will be appreciated that the network could have any suitable number of sites and that the sites may be connected to each other in any suitable way.

In the example shown in Figure 4, a location of a site in the representation of the network 20 corresponds to a geographical location of that site in the real world. The representation of the network 20 can therefore be thought of as a geographical representation of the network.

In the present example, a geographical location of a site is specified in terms of latitude and longitude of that site, although it will be appreciated that any other suitable coordinate system or method for specifying a geographical location of a physical site may be used. In various examples, the position of the sites in the representation of the network 20 is mapped according to a predetermined scaling ratio, for example 1:5000, 1:10000, 1:25000, 1:50000, and the like, although it will be appreciated that any other suitable scaling ratio may be used.

In some examples, a size of a site in the representation of the network 20 is indicative of the number of items of network equipment (e.g. the number of nodes), located at that site.

For example, as shown in Figure 4, the sites 50, 52 and 56 are larger than the site 54 thus indicating that the sites 50, 52, and 56 have more items of network equipment (e.g. nodes) associated with those sites than the number of items associated with the site 54. More generally, in some examples, the size of a site is dependent upon a number of nodes associated with that site.

In some examples, an array comprising a plurality of cells is generated and the cells of the array arranged with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network. In the context of the array, a cell shouldbe**derstood to takeamore general meaningof a unit in the array rather thana more specific radio cellular telccoms defmition of the term. The arrangement of the array with respect to the sites will now be described in more detail with reference to Figures 4 and 5.

Figure 5 is a schematic diagram of a square array of cells and a representation of the network 20. In particular, Figure 5 shows a square array 70 comprising 49 cells. In the example shown in Figure 5 a centre cell 72 is shown located at cell position (0, 0) with positions of cells in the horizontal (x) direction and vertical (y) direction labelled more generally as (x, y) with respect to the centre cell 72. It will be appreciated that cells of the array could be any suitable tessellating or non-tessellating shape such as hexagonal, triangular, and the like, and the shape of the array may be any suitable corresponding shape.

Additionally, it will be appreciated that the cells of the array could be referenced in any suitable manner as appropriate.

As mentioned above, in some examples, the array is arranged with respect to the sites so that each of the sites is associated with a respective location on the array. For example, referring to Figure 5, the site 50 is located at cell (1,0), the site 52 is located at cell (3,2), the site 54 is located at cell (3,1) and the site 56 is located at cell (3,0). In some examples, a cell may be associated with one or more sites. In the present example, cell (-1,4) is associated with two sites, cell (-1,3) is associated with seven sites, cell (0,3) is associated with nine sites and cell (3,-3) is associated with three sites. Flowever, it will be appreciated that a cell may be associated with any suitable number of sites and that some cells (such as cells (-1,0), (1,-2) of the present example and the like) may not be associated with any sites. In other words, some cells can be empty.

In some examples, the number of sites associated with a cell is dependent upon the size of a site. In some examples, the size of each site is detected and, if a site has a size larger than a predetermined size threshold, then a cell at a position which corresponds with the location of that site is arranged to only comprise that site (such as, in the present example, cells (1,0), (3,0) and (3,2)). However, cells associated with sites which have a size smaller than the predetermined size threshold can comprise more than one site (such as, in the present example, cells (-1,-i), (-1,3), (0,3), and (3,-3)). If there is a situation in which locations (in the geographically mapped network representation) of two or more sites substantially correspond and at least one of sites has a size greater than the predetermined size, then these sites can be placed in adjacent cells. However, it will be appreciated that the sites may be associated with cells in any other appropriate manner, for example, being placed in a cell within a predetermined threshold distance of a corresponding location in the geographical rcprcscntationofthe.network.

In some examples, the array is generated in dependence upon detected attributes of the geographical representation of the network. In some examples, the density of sites in the geographical representation is detected using known techniques and the array generated so that the granularity of the array is dependent upon the detected density of the sites in the network. More specifically, a mean average density in terms of number of cells per predetermined unit area can be detected. In some examples, the granularity of the grid (array) is based on the number of sites in the network and proximity of the sites to each other.

In some examples, the granularity of the grid is determined by generating a first list and second list of the geographical sites. The first list comprises the sites arranged with respect to longitude and the second list comprises the sites arranged with respect to latitude.

For each list, the shortest distance between adjacent sites is calculated according to known techniques. The granularity of the array (grid) is based on the smaller value of the shortest distance calculated from the first list and the second list. For example, the size of the cell could correspond to the smallest distance calculated from the first and second list or any integer multiple of the smallest distance, although it will be appreciated that other appropriate multiples could be used.

In the context of the examples described herein, the granularity of the array should be taken to be indicative of the number of cells in the array and the respective sizes of the cells.

For example, for a given overall size of array (i.e. for an array covering a predefmed array) an array having a higher degree of granularity would have a larger number of small cells, and an array having a lower degree of granularity would have a smaller number of larger cells. The predetermined unit area can take any suitable value and can be user selected or generated in dependence upon the scaling ratio at which the geographical representation is generated as appropriate. As mentioned above, the array of the present example is generated so that a predetermined cell of the array corresponds to a predetermined location defined with respect to the network. Although in some cases, the predetermined location defined with respect to the network may correspond with the location of a site in the network, this need not be the case and the predetermined position can correspond to any suitable location defined with respect to the network.

In some examples, the centre of the network is detected and the predetermined location corresponds to the centre of the network. For example, referring to Figure 4, the centre of the network is schematically labelled with a dot 65. In some examples, the centre of the network is taken to be the so-called "centre-of-mass" of the geographical network which is calculated,.. with the positions of.each..of the.sites being.weighted..according to the. size of the site (e.g. number of nodes at that site). In some examples, the centre of mass (CofM) of the geographical network representation is calculated according to CoJM = Eqn. 1 where m is the relative size of each site, R is a vector specifying the position of that site, i identifies each site in the network and ii is the total number of sites. In other examples, the centre of the network is defmed as the geographical centre of the network without any weighting of the sites according to size. However, it will be appreciated that any other suitable method of calculating the centre of the network could be used. Additionally, it will be appreciated that any other suitable position defined with respect to the network could correspond to the predetermined location. As mentioned above, the position of the predetermined location may or may not correspond with a location of a site as this will depend on the method used to define the predetermined location.

As mentioned above, the array of the present example is generated so that a predetermined cell corresponds to the predetermined location. In some examples, the predetermined cell is a central cell of the array such as the centre cell 72. For example, referring to Figures 4 and 5, the array 70 is shown with the centre cell 72 positioned to correspond with the centre of the geographical network representation as indicated by the dot 65 in Figure 4. However, it will be appreciated that the predetermined cell could be any other cell of the array and that the predetermined cell could correspond with any other suitable location defmed with respect to the network.

In some examples, each cell of the array is queried in a predetermined order so as to detect whether each cell is occupied by one or more sites of the network. Additionally, for each cell that is detected as being occupied, the sites associated with the occupied cell are moved to a cell closer to the predetermined cell if the cell closer to the predetermined cell is detected as being unoccupied. This will now be described in more detail with reference to Figures 6 to Ii.

Figures 6 to 11 illustrate the movement of sites of the network according to the method of the present example. In the present example, the array comprises a plurality of concentric subsets of cells arranged concentrically around the predetermined cell, with each concentric subset having a respective radius associated with a distance of the cells of that subsetftomthe..predeterminedeell.

Referring to Figure 6, a first concentric subset 100 (indicated by the shaded cells) is shown. The first concentric subset 100 comprises the cells (-1,-i), (0,-I), (1, -1), (-1,0), (1, 0), (-1,1), (0,1), and (1, 1). The first concentric subset 100 has a radius of 1 defined with respect to the centre cell 72, which in the present example corresponds to the predctennined cell mentioned above.

Referring to Figure 8, a second concentric subset 150 (indicated by the shaded cells) is shown. The second concentric subset 150 comprises the cells (-2,-2) to (2,-2) and (-2,2) to is (2,2) in the horizontal direction, and (-2,-l) to (-2,1) and (2,-l) to (2,1) in the vertical direction. The second concentric subset 150 has a radius of 2 defmed with respect to the centre cell 72, which in the present example corresponds to the predetermined cell mentioned above.

Referring to Figure 11, a third concentric subset 200 (indicated by the shaded cells) is shown. The third concentric subset 200 comprises the ce].ls (-3,-3) to (3,-3) and (-3,3) to (3,3) in the horizontal direction, and (-3,-2) to (-3,2) and (3,-2) to (3,2) in the vertical direction.

The third concentric subset 200 has a radius of 3 defined with respect to the centre cell 72, which in the present example corresponds to the predetermined cell mentioned above.

Although the example described with respect to Figures 6 to 11 shows three concentric subsets, it will be appreciated that any suitable number of concentric subsets could be used depending on the size andlor granularity of the array.

As mentioned above, in the present example, each of the cells is queried in a predetermined order. In some examples, the predetermined order comprises querying cells of a concentric subset having the smallest radius and querying cells of subsequent concentric subsets in order of increasing radius. Referring to Figures 6 to 11 the cells of the first concentric subset 100 are queried, then the cells of the second concentric subset 150 and then the cells of the third concentric subset 200.

More specifically, with reference to Figure 6 a cell adjacent to the centre cell 72 and vertically above the centre cell (i.e. the cell (0,1)) is queried to detect if that cell comprises one or more sites. More generally, for each concentric subset, a cell of that subset located in a substantially vertical direction above the predetermined cell is queried before other cells in that subset.

As can be seen from Figure 6, the cell (0,1) does not comprise any sites, i.e. cell (0,1) is unoccupied (empty), and so processing proceeds to querying the next Oell. In the present example, the cells of each concentric subset are queried in sequence in a clockwise direction.

In other w...ords, referring to. Figure 6, the next. cell to be.queried is the. cell (1,1.).. However, this cell is also empty (i.e. there are no sites associated with that cell) and so processing proceeds to the next cell in the first concentric subset in a clockwise direction.

To Cell (1,0) is queried next and, as shown in Figure 6, cell (1,0) is associated with the site 50 (that is cell (1,0) is occupied by the site 50). Accordingly, it is detected if a cell closer to the predetermined cell (in this case the centre cell 72) is occupied. In the example shown in Figure 6, the centre cell 72 is not occupied by a site and so the site 50 is moved to the centre cell 72 as illustrated in Figure 7.

The querying of the cells of the first subset 100 then continues in a clockwise direction. As can be seen from Figure 7, cells (1,-l) and (0,-i) are unoccupied but cell (-1,-i) is associated with two sites (i.e. occupied by 2 sites). However, the centre cell 72 is now occupied by the site 50 as a result of being moved earlier in the processing of the first subset.

Therefore, the two sites occupying the cell (-1,1) are not moved. More generally, if the cell closer to the predetermined cell is detected as being occupied, then the sites are not moved.

The querying of the first subset then continues until all of the cells of the first subset 100 have been queried.

In some examples, the predetermined order comprises querying the predeterniined cell before any other cells are queried. If the predetermined cell is detected as being occupied, the predetermined order comprises querying cells of a concentric subset having the second smallest radius instead of querying the cells of the concentric subset having the smallest radius. In this ease, the cells of the smallest subset do not have to be queried because the sites of the smallest subset cannot be moved as the predetermined cell is already occupied. This approach can reduce processing time because fewer cells are queried. For example, if the centre cell 72 of the array shown in Figure 6 was occupied, none of the sites in the first concentric subset 100 would be moved because the centre cell 72 would be occupied, and therefore processing could move directly to querying the cells of the second subset 150 without querying the cells of the first subset.

In the present example, once the cells of the concentric subset having the smallest (or second smallest radius) have been queried, the cells of the concentric subset having the next largest radius are queried next.

Referring to Figure 8, the cells of the second concentric subset 150 are queried after the cells of the first subset 100 (radius of 1) as the second subset 150 has a radius of 2. In the present example, a cell of that subset located in a substantially vertical direction above the predetermined., cell (when considered according to a current visualisation. orientation). .is queried before other cells in that subset. In an alternative example, a cell of that subset located in a substantially vertical direction below the predetermined cell (when considered according to a current visualisation orientation) is queried before other cells in that subset. In another alternative example, a cell of that subset located in a substantially horizontal direction to the left or right of the predetermined cell (when considered according to a current visualisation orientation) is queried before other cells in that subset. It will be appreciated that any other suitable cell of that subset could be queried before other cells in that subset as appropriate and that the location of the cell that is queried before other cells in the respective subset necd not be the same for each subset.

Referring to Figure 8, the cell (0,2) is queried before other cells in the second subset 150. The cell (0,2) will be detected as being occupied as it is associated with the site 74.

Additionally, the cell (0,1) which is closer to the centre cell 72 (predetermined cell) than the cell (0,2) is unoccupied. Accordingly, the site 74 in the cell (0,2) is moved to the cell (0,1) as this cell is closer to the predetermined cell and is unoccupied. Figure 9 illustrates the positioning the site 74 after it has been moved.

The querying of the cells of the second subset 150 then continues in a clockwise direction. The next cell of the second subset 150 is therefore cell (2,-l) which is occupied by the site 76. As shown in Figure 9, the cells (1,4) and (1,0) are unoccupied and are closer to the centre cell 72 than the cell (2,-i). In other words, there are a plurality of unoccupied sites between the occupied cell (2,-i) and the predetermined cell (centre cell 72).

In some examples, if there are a plurality of unoccupied sites between an occupied cell and the predetermined cell, the sites of the occupied cell are moved to an unoccupied cell located on a line between the occupied cell and the predetermined cell. Referring to Figure 9, the cells (1,-i) and (1,0) lie on (i.e. correspond with) a line between the cell (2,-i) and the centre cell 72 (0,0) as indicated by the dashed line 80. Accordingly, in the example shown in Figures 9 and 10, the site 76 is moved to the cell (1,-i) as illustrated in Figure 10.

In some examples, where there are two or more unoccupied cells that are located on the line, then which cell the site(s) are moved to is selected at random. In other examples, where there are two or more unoccupied cells that are located on the line, which cell the site(s) are moved to is selected as being the closest cell to the predetermined cell. However, it will be appreciated that which cell the site(s) are moved to could be selected in any other appropriate manner.

In.. some* circumstances,.. such. as when there.are. a plurality of sites.of the geographical..

representation arranged in a substantially linear way with respect to the predetermined cell, moving the sites to a cell located on a line between the occupied cell and the predetermined ito cell may lead to a representation that appears with sites arranged radially or may not provide much reduction in area because there may not be many sites that are unoccupied between the occupied cell and the predetermined cell. Therefore, in some examples, if there are a plurality of unoccupied sites between an occupied cell and the predetermined cell, the sites of the occupied cell are moved to an unoccupied cell located within a predetermined threshold is distance of a line between the occupied cell and the predetermined cell.

Referring to Figure 9, dashed lines 82 and 84 indicate a threshold distance F from the dashed line 80. In this example the threshold distance is defmed parallel to the line between the occupied cell and the predetermined cell as illustrated in Figure 9.

As can be seen from Figure 9, the cell (0,4) is within the threshold distance F of the dashed line 80 and so the site 76 could also be moved to the cell (0,-I). This can mean that there are more unoccupied cells to which a site(s) can be moved, thus allowing the resultant representation of the network to be made more compact. The appearance of the sites once moved according to this example, more resembles a fan arrangement of sites rather than a linear arrangement as mentioned above. Accordingly, the compacted representation can be made more compact whilst still preserving an overall visual impression of the relationship of the sites in the network.

In another example, if there arc a plurality of unoccupied sites between an occupied cell and the predetermined cell, the sites of the occupied cell are moved to an unoccupied cell corresponding with a circular sector defmed either side of a line between the occupied cell and the predetermined cell within a predetermined threshold angle. For this example, referring to Figure 9, a dashed line 86 and a dashed line 88 each lie at an angle 0 with the line 80. The lines 86 and 88 defme edges of a circular sector with the centre of the array being the centre of the sector and the cells (1,4) and (1,0) corresponding with this circular sector. This example allows the resultant representation of the network to be made more compact whilst helping to maintain the overall visual impression of the relationship of the sites of the network. This helps the network designer appreciate the layout of the network more easily.

Figure 10 shows an arrangement of the sites once all of the cells of the second subset have been queried. Once all of the cells of the second subset 150 have been queried, the cells of the third subset 200 are queried using the techniques described above as the third subset has the next largest radius (radius of 3 unit cells).

Figure 11. schematically illustrates the positions of the sites after the third subset 200 has been queried as described above. In some examples, if a cell is detected as being occupied then the sites associated with that cell are moved to an unoccupied cell closest to the predetermined cell. Referring to the example shown in Figure 11, the sites 52 and 56 are shown located at cells (1,1) and (1,0) respectively after moving. However, in other examples, if a cell is detected as being occupied, then the sites associated with that cell are moved to an unoccupied cell closer to the predetermined cell within a cell threshold distance of the cell which is detected as being occupied. In some examples, the cell threshold distance is 3 unit cells, although it will be appreciated that any other suitable cell threshold distance could be used.

In some examples, a "line-of-sight" list of cells is generated which comprises those cells between the occupied cell (i.e. queried cell) and the predetermined cell. In other words, the line-of-sight list comprises those cells which lie on a line between the occupied cell and the predetermined cell. If all of the cells in the line-of-sight list are occupied, then cells immediately adjacent to the cells in the line-of-sight list are queried. If the cells immediately adjacent to the cells of the line-of-sight list are also occupied, then the site(s) of the occupied (queried) cell are not moved. However, if there are one or more unoccupied cells in the line-of sight list or the cells immediately adjacent to those in the line-of-sight list, then the site(s) of the occupied (queried) cell are moved to a cell closer to the predetermined cell. In some examples, the site(s) are moved to the cell closest to the predetermined cell if there are one or more unoccupied cells in the line-of-sight list or the cells immediately adjacent to those in the line-of-sight list.

Although Figures 6 to 11 have been described with the querying of the cells of each concentric subset being carried out in a clockwise direction, it will be appreciated that they could be queried in an antielockwise direction or in any other suitable sequence.

Furthermore, it will be appreciated that the order in which the cells of each subset are queried need not be the same for each subset.

Once all the cells of the array have been queried, a representation of the compacted network may be generated including the sites and edges as illustrated in Figure 12. In some examples, as mentioned above, each site comprises one or more nodes representative of a physical device located at that site, and each node is connected to one or more other nodes by s an edge. In some examples, a representation of the nodes and edges is generated and displayed based on the location of the sites after they have been moved. In other words, in some examples, a representation of the nodes and edges may be generated and displayed on the display 28 based on the layout of the sites once moved, for example based on the positioning of the sites illustrated in Figure 12.

In some examples, the representation of the nodes is generated and displayed with respect to each site based on a predetermined layout pattern dependent on the number of nodes associated with a respective site. In one example, two nodes associated with a site could be displayed in a linear fashion, three nodes associated with a site could be displayed in a triangular fashion, four nodes associated with a site in a square fashion and so on. However, it will be appreciated that they may be displayed in any appropriate way.

Figure 13 schematically illustrates a degree by which the geographical representation of the network may be reduced in size so as to be more compact. In particular, Figure 13 shows the geographical representation of the network and a compacted representation of the network 250. As can be seen from Figure 13, the compacted representation 250 has a reduced size and substantially maintains an overall visual impression of relative locations of the sites of the network.

A method of generating a representation of a network according to the present example will now be described with reference to Figures 14 arid 15.

Figure 14 is a flow chart of a method for generating a representation of a network.

At a step slOO, an array of cells is generated which comprises a predetermined cell. In the present example, the array of cells corresponds to the array 70 described above with reference to Figures 4 to 11. However, it will be appreciated that other suitable arrays could be generated.

At a step slOS, the cells of the array are arranged with respect to the sites so that each of the sites is associated with a respective location on the array and so that the predetermined cell of the array corresponds to a predetermined location defined with respect to the network.

As mentioned above, in some examples, the predetermined location can be the centre of the network, although it will be appreciated that any other suitable predetermined location could be used.

At a step silO each cell of the array is queried in a predetermined order to detect if that cell is occupied by one or more sites. In some examples, the predetermined order is the order described above with reference to Figures 4 to 11, although it will be appreciated that other suitable predetermined orders could be used.

At a step sl 15 it is detected if the queried cell is occupied. If the queried cell is not occupied then a next cell is queried according to the predetermined order at the step si 10.

However, if at the step si 15, the queried cell is detected as being occupied, then, at a step s 120, it is detected whether there are any unoccupied cells closer to the predetermined cell than the queried cell.

In other words, the steps silO and sll5 can be considered as querying a first cell of the array so as to detect whether that cell is occupied by one of more sites of the network and querying a next cell of the array according to the predetermined order if the first cell is detected as not being occupied.

If, at the step s120, it is detected that there are one or more unoccupied cells closer to the predetermined cell than the queried cell, then, at a step sl25 the site(s) associated with the queried cell are moved to an unoccupied cell closer to the predetermined cell than the queried cell. In various examples, the sites are moved according to the methods described above with reference to Figures 4 to 11.

If, at the step s120, it is detected that there are not any unoccupied cells closer to the predetermined cell than the queried cell, then, at a step s130, the site(s) of the queried cell are left in the queried cell.

The above described methods can be generalised further as illustrated by the flowchart shown in Figure 15. Figure 15 is a flowchart of a method for generating a representation of a network according to the present examples.

At a step s200, an array (e.g. array 70) is generated comprising a plurality of cells.

At a step s205, the cells of the array are arranged with respect to the sites so that each of the sites is associated with a respective location on the array and so that a predetermined cell of the array corresponds to a predetermined location defmed with respect to the network.

The predetermined cell may be the centre cell and the predetermined location may be the centre of the network as mentioned above, although it will be appreciated that any other suitable predetermined cell and predetermined location could be used.

At a step s210, each cell of the array is queried in a predetermined order so as to detect whether each cell is occupied by one or more sites of the network. In some examples, the predetermined otder is the predetermined order described above, although it will be appreciated that other suitable predetermined orders could be used.

At a step s215, for each cell that is detected as being occupied, the sites associated with the occupied cell are moved to a cell closer to the predetermined ccli if the cell closer to the predetermined cell is detected as being unoccupied.

In the examples described above, the array is a square array. However, it will be appreciated that the array could be any other suitable array.

In some examples, the array is a hexagonal array as shown in Figure 16. Figure 16 is a schematic diagram of a hexagonal array of cells used to generate a representation of a network in accordance with this example. In particular, Figure 16 schematically shows a hexagonal array 700 comprising a plurality of hexagonal cells. The hexagonal array 700 comprises a centre cell A and a plurality of concentric subsets of cells. The plurality of concentric subsets comprises a first concentric subset (cells labelled B in Figure t6), a second concentric subset (cells labelled C in Figure 16), and a third concentric subset (cells labelled D in Figure 16).

is However, it will be appreciated that any appropriate number of concentric subsets may be used. As shown in Figure 16, the first subset (cells B) has a radius of 1 unit cell, the second subset (cells C) has a radius of 2 unit cells, and the third subset (cells D) has a radius of 3 unit cells. The processing of the geographical representation using the array of Figure 16 is the same as that described above with reference to Figures 4 to 15.

The examples described herein may provide a fast and effective method of compacting a representation of a network such that key spatial characteristics, such as relative positioning of sites, are substantially preserved. This aids a user in visualising a network and thus improves the efficiency of designing a network, planning upgrades and the like. Furthermore, the runtimc of the examples described herein when implemented on a computer depends on the number of sites and the granularity of the array.

In the examples described herein, the runtime is independent of the number of edges within the network because the compaction of the representation is based on moving sites of the network. This is in contrast to force based algorithms whose complexity depends at least in part on the number of edges. In other words, the computational execution time required to implement the examples scales in a substantially linear manner with the number of sites because the computation is based on piecemeal operations on cells of an array. In contrast, the computational execution time of force based algorithms tends to scale in a non-linear way with the number of sites or nodes due to the interaction of the forces between the nodes.

Accordingly, the examples described herein may be used to improve implementation of modelling complex internet packet (IP) and/or radio handover based edge relationships where a few nodes may be meshed together to many other nodes. Here, meshed together should be taken to mean connected together, for example so as to communicate data between nodes. In this context, fully meshed should be taken to mean that each node N(i) of a full mesh of nodes N(i=1..N) is connected to every other node, Partially meshed should be taken to mean that each node N(i) of a partial mesh of nodes N(i=l..N) is connected to at least two other nodes.

The full mesh and partial mesh of nodes may communicate with each other using known techniques according to a known suitable wireless mesh network architecture.

In the examples described above, the network may be a telecoms network and each site may correspond to a physical location of network equipment in the telecoms network.

However, it will be appreciated that the examples described herein may be applied more generally to any suitable network. In other words, the examples described herein may be applied to any data which may be represented as nodes and/or nodes and edges.

Additionally, it will be appreciated that the techniques described herein may be applied to all of the sites of the network, or only some of the sites of the network.

Additionally, it will be appreciated that the techniques described herein could be applied to all of the network or only part of the network with the predetermined location being selected accordingly.

Furthermore, it will be appreciated that while the examples described above have been described with reference to a representation of sites in two dimensions, the techniques described herein may be more generally applicable to representations of data in three dimensions, with cells being queried in order of shells at a predetermined radius. For example, a cubical array comprising a plurality of cubical cells could be used (where each cell is a cube). In this example, cells corresponding to faces of a cube having a radius of one cell from the predetermined cell (e.g. the central cell), that is cells adjacent to the predetermined cell, are queried first according to a predetermined order such as those described above. Cells corresponding to faces of a cube having a radius of two cells from the predetermined cell would be queried next, with cells of the faces of a next largest cube then being queried and so on. In other words, in this example, the cells which correspond to faces of cubes of a predetermined size can be considered as shells at a predetermined radius, with the shells being queried in order of increasing radius. However, it will be appreciated that other suitable three dimensional arrays (such as a tetrahedral array of tetrahedral cells, an octahedral arrays of octahedral cells and the like) together with suitable corresponding shells could be used.

Accordingly, it will be appreciated that the techniques described herein may be applied to any two or three dimensional representation of data in which one or more sites may be specified in two or three dimensions.

In examples, a schematic representation of a network may be generated from a given geographical representation of the network using the techniques described herein.

A computer system which may implement the example methods described herein will now be described with reference to Figure 17.

Figure 17 schematically illustrates a computer system 2000. The computer system 2000 comprises a system unit 1000, and a plurality of peripheral devices. The system unit 1000 comprises: a processor 1005; a memory 1010; a graphics interface 1015; a data bus 1020; a hard disc drive (HDD) 1025; a removable storage medium drive 1030; and an input/output (I/O) port 1035. The peripheral devices comprise a keyboard 1040; a mouse 1045; and a display 1050.

The processor 1005 is operable to receive control signals from the keyboard 1040 and mouse 1045 so as to control operation of the system unit 1000. However, it will be appreciated that other suitable input devices may be used to control operation of the system unit 1000 such as a track ball, touch input device (e.g. in cooperation with the display 1050), and the like.

The processor 1005 is operable to communicate bidirectionally with the hard disc drive 1025, removable storage medium 1030, and input/output port 1035 via the data bus 1020. In some examples, the removable storage medium is a DVD-ROM although it will be appreciated that other suitable removable storage media such as CDROM, CD-ZR, CD.RW, DVDR, DVD-RW, Blu-ray disc, memory stick, and the like could be used. Software for controlling the system unit may be stored on the HDD 1025 and/or the removable storage medium 1030 in accordance with known techniques.

The input/output port 1035 is operable to allow the system unit to communicate with one or more peripheral devices, such as a printer, scanner, memory stick, and the like, although it will be appreciated that any suitable peripheral device could be used. In some examples, the input/output port 1035 comprises a universal serial bus (USB) port for communicating according to a USB protocol. However, it will be appreciated that the input/output port 1035 could comprise any other suitable interface (wired or wireless e.g. IEEE 1394, IEEE8O2.i 1, ethernet and the like) and allow the system unit 1000 to communicate according to any suitable protocol. In some examples (not shown), the system unit comprises a network interface (wired or wireless) for communicating with a network such as the internet or a local area network (LAN), although any suitable network interface could be used.

The processor 1005 is operable to write data to andlor read data from the memory 1010 according to known techniques so as to allow the processor 1005 to implement instructions to control operation of the system unit. In some examples, the memory 1010 comprises dynamic random access memory (DRAM) although it will be appreciated that any other suitable form of memory could be used.

The processor 1005 is operable to generate graphics data and communicate the graphics to the graphics interface 1015. In response to the graphics data generated by the processor 1005, the graphics interface is operable to generate control signals to control the display of the graphics data on the display 1050.

In some examples (not shown), the system unit 1000 comprises an audio interface and the processor 1005 is operable to generate audio data to cause the audio interface to output the audio data to a suitable audio reproduction device, such as one or more loud speakers, headphones and the like, although it will be appreciated that any other suitable audio reproduction device could be used.

Although Figure 17 shows an example of a general purpose computer which may be used to implement the examples described herein, it will be appreciated that other suitable general purpose computers could be used to implement the described examples.

The various methods set out above may be implemented by adaptation of an existing computing apparatus, such as the computer system 2000, for example by using a computer program product comprising processor implementable instructions stored on a data carrier (removable storage medium) such as a floppy disk, optical disk, hard disk, PROM, RAM, flash memory or any combination of these or other storage media, or transmitted via data signals on a network such as an Ethernet, a wireless network, the Internet, or any combination of these of other networks, or realised in hardware as an ASIC (application specific integrated circuit) or an FPGA (field programmable gate array) or other configurable circuit or bespoke circuit suitable to use in adapting the existing equivalent device.

In conclusion, although a variety of examples have been described herein, these are provided by way of example only, and many variations and modifications on such examples will be apparent to the skilled person and fall within the spirit and scope of the present invention, which is defined by the appended claims and their equivalents.